The vertices of a trapezoid are shown below.
(0, 8), (6, 16), (6, 12), (0, 16)
Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2 ?
A.
(2, 18)
B.
(12, 24)
C.
(0, 4)
D.
(4, 3)

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The vertices of a trapezoid are shown below.
(0, 8), (6, 16), (6, 12), (0, 16)
Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2 ?
A.
(2, 18)
B.
(12, 24)
C.
(0, 4)
D.
(4, 3)

Mathematics

Stacey Warren - Expert brainly.com

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A dilation with a factor of 1/2 will make the figure bigger or smaller?

rayman5766

2 years ago

bogger i would hope

mathmate

2 years ago

A dilation factor of 2 will make the figure twice as big as the original,
a dilation factor of 3 will make the figure three times as big as the original,
So rethink for a factor of 1/2!

rayman5766

2 years ago

oh i think i see so the figure would be smaller i guess

mathmate

2 years ago

So do we agree that a scale factor of more than one will make the image bigger, and a scale factor of less than one will shrink the image (even it's called dilation).

rayman5766

2 years ago

yes we can

mathmate

2 years ago

Good!
So a factor of 1/2 will shrink the original to what size?
For example, you have a point P(1,2).
Dilation factor of 2 will bring it to P'(2,4).
Dilation factor of 3 will bring P'(3,6).
What would be the coordinates of P' using a dilation factor of 1/2?

rayman5766

2 years ago

1,4?

mathmate

2 years ago

Please explain how you arrived at (1,4).

mathmate

2 years ago

Remember that 1/2 means \(\frac{1}{2}\), or 0.5.

rayman5766

2 years ago

actual would it be 1,1

mathmate

2 years ago

Please explain how you arrived at (1,1).

mathmate

2 years ago

(note: I will ask you to explain even if the answer is correct!)

mathmate

2 years ago

(note: I will ask you to explain even if the answer is correct, so stop guessing)

rayman5766

2 years ago

sorry i was using multiplication for my answers but that would make more sens 1/2 is 50 so in dilation it would be 0,5 sorry for my stupidity

mathmate

2 years ago

So please explain how you got (1,1).

rayman5766

2 years ago

well i thought i seen a pattern with the 2,4 being 4 2x2 would be 4 and 3 x 2=6

rayman5766

2 years ago

so i thought 1 would equal 1.1 but i forgot it was a 1/2 wich would make it 0.5 sorry i think of some other thing wich would make it the answer

rayman5766

2 years ago

also i keep putting wich and now which

mathmate

2 years ago

Good, the fact is that each of the (x,y) coordinates must be multiplied by the scale factor.
For example, if we apply a factor of 1.5 to P(2,5), we would get P'(2*1.5, 5*1.5)=P'(3,7.5).
So can you try again?

rayman5766

2 years ago

i meant not

rayman5766

2 years ago

ok i can try

mathmate

2 years ago

Not a problem unless you order a sandwhich at a restaurant! lol

rayman5766

2 years ago

ha good one you see when i think of math i think of possibility's so i think of this which would make that

rayman5766

2 years ago

be the answer

mathmate

2 years ago

Just in case our original question was lost:
For example, you have a point P(1,2).
Dilation factor of 2 will bring it to P'(2,4).
Dilation factor of 3 will bring P'(3,6).
What would be the coordinates of P' using a dilation factor of 1/2?

rayman5766

2 years ago

so i get confused and make a dump aswer which makes me look like an idiot

mathmate

2 years ago

The only dumb answer is the one that was never made!

rayman5766

2 years ago

2*1.2 and 3*1.5 =

rayman5766

2 years ago

i didn't put the answer becaues i am trying to make sure i am going in the right path here so am

rayman5766

2 years ago

wait would my answer be A

mathmate

2 years ago

The answer to \(my\) question, P(1,2) with a factor of 0.5 is
P'(1*0.5, 2*0.5) = P'(0.5,1)
(use a calculator if you need to)
Understand how the above problem was solved before thinking about the problem you are trying to solve.
Math is about understanding. We should always understand how to solve a class of problems BEFORE attempting exercises on the topic. Guessing will only make math hard, for now and for the future.

rayman5766

2 years ago

wow that was some hard core wisdom you just said but you are correct

rayman5766

2 years ago

also that would make sens knowing 1/5 is 0.5 oki thik i get it

mathmate

2 years ago

1/2 = 0.5, 1/5\(\ne\) 0.5

rayman5766

2 years ago

oh sorry i know that

rayman5766

2 years ago

i put a 5 and not a 2my bad

rayman5766

2 years ago

but one more thing were does the 3 you put up there come from '

mathmate

2 years ago

Just in case our original question was lost:
For example, you have a point P(1,2).
Dilation factor of 2 will bring it to P'(2,4).
Dilation factor of 3 will bring P'(3,6).
What would be the coordinates of P' using a dilation factor of 1/2?
If this is what you meant, they were examples